2023 KCPE Mathematics Commonly Tested Questions; Key Areas

| April 28, 2024 | Teachers' Resources | No Comments

COMMONLY KCPE TESTED QUESTIONS

MATHEMATICS

200 PREDICTION QUESTIONS

                                              Time: 2 Hours 30 Mins

  1. Which of the following is ten million ten thousand and ten?
    1. 10 010 100
    2. 10 010 010
    3. 10 100 010
    4. 10 001 010
  2. What is the 299.995 rounded off to the nearest two decimal places?
  3. How many days are there between 5th February and 4th April of a leap year?
  4. What is the place value of digit 9 in sum of 428 657 and 368 725?
  5. What is the value of 62 +42 +3 (2+4)?

2 x 7

  1. Chebet bought the following items from a shop

2-2 litre bottles of cooking oil @ 120 per litre

3kg sugar @ sh. 105

45kg rice @ sh. 80 5 rolls of tissues for sh. 100

If she paid using 2 – 1000 shilling note, how much balance did she get?

  1. The triangle ABC below is drawn to scale.

What is the size of angle ACB?

  1. What is the sum of the square of 1% and the square root of 2%? %
  2. What is the next number in the sequence? 1, 4, 9, 16,
  3. What is the simplified form of

3(2x + 3y) + 2(4x + 5y)

  1. The table below shows arrival and departure timetable for the train from towns A, B, C and D.
Town Arrival Departure
A   7.30am
B 9.15am 9.30am
C 11.25 am 11.35am
D 1.25pm  

How long did it take the train to travel from town B to town D?

  1. The area of a square plot of land was 625m?.

What was twice its perimeter?

  1. Construct a triangle ABC such that line AB-4cm, BC-5cm and angle BAC = 90°. Draw a circle touching the points ABC. What is the radius of the circle?
  2. What is the value of

12/5 ÷ 11/5 + 2½ of 1/3

  1. Salat bought a generator for sh.20 400 after getting a 15% discount. What was the marked price of the generator?
  2. Three streetlights light at an interval of 6min, 8min and 12min. If they all started at

8.00am. At what time did they light again?

  1. A cylindrical container with a radius of 28cm contain water to a height of 50cm. How many litres of water does it hold?
  2. The fractions 2/3, ¾, 3/8 and 2/5 are to be arranged in order from the smallest to the largest. What is the correct order?
  3. Which of the following characteristics of quadrilaterals is both for rhombus and square?
    1. Has one pair of parallel lines
    2. Diagonals are equal
    3. All the angles are right angle.
    4. Diagonal bisect at right angle.
  4. The table below shows the number of pupils who joined class eight in Kahutha location.
Year 2016 2017 2018 2019 2020
No. of pupils 386 425 369 438 398

Which two consecutive years was the number highest?

  1. What is 74296 divided by 37?
  2. What is the value of t in the equation 3/5(10x+15)-10 = 20 ?
  3. The diagram below shows a net of a solid.

When folded which solid will be formed

  1. A company hired 18 men to do a job in 24 days. How long did it take if 6 men did not turn up?
  2. Which of the following sets of measurements will form a right angled triangle?
  3. The mass of an empty pick up is 0.9 tonnes. The pick up was loaded with 20 bales of maize flour each with 12-2kg packed. It is also loaded with 20-50kg bags of rice. What is the mass of the loaded pickup in kg?
  4. Ochieng bought a cow at sh.24 000. He later sold it making 18% profit. What was the selling price?
  5. Jamal deposited sh.120 000 in a commercial bank that charged simple interest at the rate of 8 percent per annum. How much interest did the money earn after two years?
  6. A public rally was attended by 380 men. The number of women was thrice that of men but half that of children. How many people attended the rally?
  7. The marked price of a TV is sh.24 000. The hire purchase price is 25% more than the marked price. Wambua bought it on hire purchase paying a deposit of sh. 12 000 and the rest in 12 equal monthly instalment. How much is each instalment?
  8. The diagram below shows an isosceles triangle.

If the perimeter is 36cm what is the area of the triangle?

  1. Parsaloi read 2/5 of a book on Monday and 1/7 on Tuesday and the rest on Wednesday.

What fraction of the book did he read on Wednesday?

  1. What is the value of 72 + 0.6 – 0.12 ?

0.2

  1. A saleslady earn a basic salary of sh. 15 000. She is also paid 5% commission on all the sales she makes in a month. How much money did she earn in a month she sold good worth sh. 250 000?
  2. A road in a map is drawn to scale 1: 500 000. What is the actual length of the road which is drawn to scale of 6cm?
  3. Three girls Nancy, Nelly and Nimo contributed a total of sh.325 to buy a gift for their friends. Nancy contributed sh.30 more than Nelly. Nimo contributed sh.25 more than Nancy. If Nancy contributed sh.m, which of the following equation will be used to find the amount Nancy contributed?
  4. In a school there were 840 pupils last year. This year the numbed increased by 25% What is the new population?
  5. The length of a rectangular plot is 240m and the width 160nt. What is the area of the plot in hectares?
  6. The mean age of seven pupils is 12. If the age of the first 6 is 8, 10, 11, 18, 16, 8, what is the age of the seventh pupil?
  7. A motorist covered a distance of 144km in two hours. What was his speed in m/s?
  8. What is the surface area of an open tank of diameter 1.4m and a height of 1.2m in mo?
  9. A watch loses 30 second every hour. If it was set right on Monday 8.30am, at what time did it shows on Tuesday 8.30am?!
  10. The ratio of boys to girls in a school is 3:4 if there are 120 less boys than girls, how many pupils are there in that school?
  11. A rectangular tank measures 0.5m by 0.6m by 0.8m. How many litres of water does it hold when half full?
  12. The table below shows how Wangira scored in an exam.
Subject Math Eng Kis Sci SST
Score out 39 30 36 42 33

If this information was put on a pie chart, what angle would represent Maths?

  1. The table below shows the charges of sending money order.
Value of order Commission
Upto 1000 54
1001 – 2500 86
2501 – 5000 124
5001 – 10000 182
10001 – 20000 246

Mugambi sent two money orders one worth sh.12 000 and the other worth sh. 7 500. How much money did he pay at the post office?

  1. What is the value of 2ab – b

3b if a=2 and 6 = 6?

  1. What is the sum of the next two numbers in 7, 14, 25, 38,___,___
  2. What is 65% as a ratio in its simplest form?
  3. A lorry was loaded with 40 bags of beans each weighing 110kg. When half of the was off loaded, the lorry weighed 5.7 tonnes. What is the mass of the empty lorry?
  4. How many groups of thousands are there in the total value of digit 4 in the number 548 928 671?
  5. What is ninety eight million, ninety eight thousand and ninety eight in numerals?
  6. What is the next number in the pattern?

209, 168, 131, 100, 71, ________

  1. What is 6/13, 9/14, 8/15, and 11/17 arranged in an ascending order?
  2. What is 28. 2586 rounded off to the nearest hundredths?
  3. What is the place value of digit 6 in the number 962 534?
  4. What is the value of 8¼ + 21/3 of  32/9 ÷ 11/6 ?
  5. What is the value of:

0.87 + 51.3 – 0.09 + 0.2?

  1. Which of the following numbers is divisible by 11?
  2. The area of a square plot of land is 2 809m2. Find the length of one side.
  3. The population of a country is 46 005 818. If 15 589 746 are women and 21 934 834 are children, how many men are in the country?
  4. In the figure below, line AB is parallel to line CD and line PQ is a transversal line.

Which of the following statements is true?

  1. Angle b and g are corresponding angles.
  2. Angle a and e are co-interior angles.
  3. Angle h and g are vertically opposite angles.
  4. Angle c and e are alternate angles.
  5. The area of a triangular piece of land is 22.5 Ares. It has a base length of 250 metres.

What is its height in metres?

  1. Which of the following properties is true in both a rhombus and a parallelogram? A. All sides are equal.
    1. The sum of interior angles adds up to four right angles.
    2. Diagonals bisect each other at right angles.
    3. Each interior angle is a right angle.
  2. The total length of a barbed wire round a square piece of land is 144m. What is the area of the piece of land in square metres?
  3. Simplify:

3/5 (40x − 25y) + 2/3 (18x − 21y)

  1. What is the value of a (3c – 2b)

d when a = 2, d = 5, b = 3 and c = 4?

  1. What is the value of letter y in the equation below? 5(3y − 2) = 2(3y + 13)
  2. Simplify the inequality 2(x − 1) < x + 4
  3. The height of the tank below is 1.2 m. It has water upto a depth of 70 cm. How many litres are needed to fill the tank?
  4. Construct triangle PQR in which line PQ = 6.5cm, angle QPR = 30° and angle PRQ = 40°. Draw a circe that touches points P, Q and R. What is the radius of the circle?
  5. The top of a 17m ladder leans on a vertical wall with its lower end touching the ground. Which one of the following sets of measurements represents the height of the wall and the horizontal distance from the ladder to the wall?
  6. What is the total value of digit 8 in the decimal number 3.52842?
  7. Which one of the following fractions will give a recurring decimal?
  8. Work out:

√0.0324

  1. A bus travelled from Mombasa to Nairobi, a distance of 468km. Later on, the bus went another 281km to Nakuru and then further 96km to Kericho. What distance in kilometres was covered by the bus altogether?
  2. A lorry carries 378 bags of rice in one trip. Each bag of rice is 25kg. If the lorry makes 18 trips, how many tonnes does the lorry transport?
  3. In a coffee plantation, 28 080 coffee seedlings were planted in 156 rows. How many coffee seedlings were planted in each row?
  4. Three bells ring at intervals of 24 minutes, 30 minutes and 40 minutes. The bell rang together at 1145hrs. At what time in am/pm will they ring together again?
  5. Kipkoech’s stride is 5/8, of a metre. How many strides will he make to cover a distance of 80m?
  6. A man spent 3/8 of his salary on food, 1/5 on clothing, ¼ on other expenses and saved the rest. What fraction of his salary did he save?
  7. What is the GCD of 28, 63 and 84?
  8. A matatu left Busia for Nairobi at 2045hrs on Wednesday. The journey took 8 hours 55 minutes. What time and day did it reach Nairobi?
  9. What is the square of 2¼ ?
  10. What is 11/16 as a percentage?
  11. Construct triangle PQR where line PQ = 9cm, QR-12 cm and angle PQR is a right angle. Draw a circle touching the sides of the triangle. Measure the radius.
  12. The radius of a bicycle wheel is 21cm. How many turns will it make to cover a distance of 6.6km?
  13. The cost of a plot in Isinya in the year 2020 was sh. 400 000. After one year, the cost of the plot appreciated by 35%. What was the cost of the plot in the year 2021?
  14. A rectangular piece of land measures 32.4m in length and 26.8m in width. Kiba fenced this land with four strands of barbed wire. What was the length of the wire used?
  15. In the year 2021, covid related deaths in a certain country was 3 500. In the year 2022, this number reduced by 26%. How many people died of covid in the year 2022?
  16. The table below show the marks scored by a pupil during a test.
SUBJECT MATHS ENGLISH KISW SCIENCE SIST
SCORE 88 84 68 90 70

If a pie chart was to be drawn, what angle would represent Kiswahili?

  1. There was 1 800 litres of water in a tank. During construction, 68% of the water was used. How much water was left in the tank?
  2. What is the area of a circle whose radius is 28cm?
  3. The following are characteristics of a quadrilateral;
    1. Diagonals are not equal
    2. Some angles are equal
  • Interiror angles add up to four right angles
  1. All sides are equal.

The quadrilaterial described above is a;

  1. In a certain factory 3/5 of the employees are women. On a day when 3/20 of the women were absent, 306 women were present. How many men are there in the factory?
  2. The table below shows Wanjala’s expenditure for the month of December 2021. The information on the expenditure on clothing is not indicated.
 Item  Rent  Food  Saving  Clothing
 Amount  Sh. 6 000  Sh. 5 000  Sh. 4 000  

A pie chart was drawn to represent the information above. If the angle representing the expense on food was 100°, how much was used on clothing?

  1. A length of 3.2cm era on a scale drawing represents an actual length of 9 600m. What is the scale used?
  2. If a tray holds 30 eggs, on which day did the farmer collect 1050 eggs?
  3. The mean mark scored by five pupils in an examination was 82. If the marks of four of them were 84, 96, 78 and 64, what was the score of the fifth pupil?
  4. Ole Munyere shared a number of cows: To his four children. Their shares were Timothy 0.3, Gloria 0.11, Sein 0.19 Naiserian 0.17. If the children gota total of 462 cows, how many cows did he remain with?
  5. Write 30030030 in words

 

  1. Work out:

4/5 × 3¾ − 3/7 ÷ 5/14 + 3/10

  1. What is the total value of 80.4 − 46 + 4.54 ?

0.4

  1. What is the value of digit 2 in the quotient of 3.40068 and 17?
  2. How many days are there between 20th May and 20th July?
  3. Which of the following is the smallest digit that can be added to 7395 to make it divisible by 11?
  4. The below shows a school farm. Adhiambo walked around the farm four times. What distance did she cover?
  5. A map was drawn using a scale of 1:1000. Calculate the actual length of a road 5

cm long on the map in metres.

  1. Which quadrilateral has only one pair of parallel lines?
  2. What is the value of: 2 x 0.05 of (6.4 − 3.2) − 0.32 ÷ 2
  3. A bus arrived in Nairobi from Mombasa at 3.00am on Tuesday. If it took 8 hours 50min to travel from Mombasa to Nairobi, when had it left Mombasa?
  4. What is the next number in the sequence below?

6, 13, 24, 39, ________________________

  1. In the year 2006 a factory was supplied with 4800 parallel lines? bags of maize. This was 20% less than what was received in 2005. How many bags were supplied in 2005?
  2. What is the value of

− 9?

  1. The mass of a bag decreased by 30kg to 120kg what is the percentage decrease?
  2. In the figure below EFGH, GJK and MJH are straight lines. FM is parallel to GK. Angle EFM = 128° and angle MJK = 62°. What is the size of angle GHJ?
  3. Ann received a salary of sh. 30000 per month. She uses 3/20 of it for rent, for school fees and saves the rest. How much more does she save than use on rent?
  4. Three containers are capable of holding 54 litres, 72litres and 90litres respectively. Find the capacity of the largest container which can be used to fill each one of them exactly?
  5. The hire purchase price of a motor bike is sh. 97860. Allan paid a deposit of sh.

3000 and 30 equal monthly installments. How much was each instalment?

  1. What is the sum of faces, edges and vertices of an open rectangular prism?B
  2. What is the smallest number when divided by 12, 20 or 36 the remainder is always 4?
  3. Construct triangle PQR in which line PQ = 6.5cm, angle QPR = 30° and angle PRQ = 40°. Draw a circe that touches points P, Q and R. What is the radius of the circle?
  4. Four men working at the same rate would take 6 days to clear a piece of land.

How many more men are needed in order to complete the work in 4 days?

  1. What is the total value of digit 8 in the decimal number 3.52842?
  2. A wheel covers a distance of 7.92km after making 3000 revolutions. What is the radius of the wheel in metres?
  3. A trader sold 1.5 tonnes of rice in 3kg packets. How many packets were sold?
  4. What is the possible value of y in the inequality below 3y + 6 > by − 9?
  5. The cost of a plot in Isinya in the year 2020 was sh. 400 000. After one year, the cost of the plot appreciated by 35%. What was the cost of the plot in the year 2021?
  6. The masses of 8 pupils were recorded as 35kg, 32kg, 28kg, 25kg, 38kg, 40kg and 37kg. What was the median mass?
  7. What is the value of 8 x 0.084?

16.8

  1. Draw triangle ABC in which AB=6cm, BC= 10cm and AC = 8cm. Draw a circle to touch the points of the triangle ABC. What is the radius of the circle?
  2. A bottle holds 2.816litres of juice. If it has a height of 14cm, what is the diameter of the bottle in centimetres?
  3. What is 7869.85872 rounded off to the nearest hundredths?
  4. What is the value of x in

2(x+5) − 14 = 36

  1. On a certain day a trader spent sh. 8000 to buy 20 textbooks and then sold them making a profit of 15%. For how much did the trader sell each textbook?
  2. The total length of a barbed wire round a square piece of land is 144m. What is the area of the piece of land in square metres?

 

  1. Which of the following will not form a right angled triangle?
  2. Zainabu bought the following items from a wholesale shop

2kg of rice @ sh. 150

  • – 2kg packets of wheat flour @ sh 140

1kg of sugar @ sh. 124

2packets of tea leaves for sh. 120

She paid using two notes of sh. 500. How much balance did she receive?

  1. Agnes and John shared money in the ratio of 5:3. Agnes got sh. 1800 more than John. How much money did John get?
  2. Express 12½% as a ratio
  3. Omondi covered 325km. If he left Nairobi at 8.15am and reached Meru at

11.30am, calculate the speed?

  1. A rectangle measuring 32cm long and 18cm wide has an equal area as a square. Find the perimeter of the square?
  2. What is the area of a circle whose radius is 28cm?
  3. Find the value of 3c + 4d + 2b given that d = 3, c = ½b and b = 2

(cd)

  1. In a certain factory 3/5 of the employees are women. On a day when 3/20 of the women were absent, 306 women were present. How many men are there in the factory?
  2. An open cylindrical tin has a diameter of 14cm and has a height of 10cm. What is its capacity in millilitres when half full?
  3. The mean mass of 5 girls is 15kg. The average mass of the first three girls is 17kg. What is the total mass of the remaining two girls?
  4. A square plot has an area of 3600m2. It was fenced round using 4 strands of wire. What length of wire was needed?
  5. Which of the following is not a property of a square?
  6. Ole Munyere shared a number of cows: To his four children. Their shares were Timothy 0.3, Gloria 0.11, Sein 0.19 Naiserian 0.17. If the children gota total of 462 cows, how many cows did he remain with?
  7. What is 7090315 written in words?
  8. What is the value of 300 − 75 ÷ 15?

5

  1. What is the value of: 4/5 − 1/3 of ¾ +5/6 ?
  2. What is the value of 0.324 ÷ (0.03 x 0.6)?
  3. What is 570.9685 correct to the nearest lenth?
  4. What is the measure of the obtuse angle KLM drawn below?
  5. What is the square of 2¼?
  6. Mavia bought the following items from the shop

4 packets of sugar @sh 107

2kg tomatoes @sh 88

½ kg of meat @sh 400

  • bottles of soda @sh 35

How much balance did she get from sh 1000?

  1. What is 3/8(24x −16y) + 4y in the simplest form?
  2. What is 3/8, 4/5, 7/20, 3/10 arranged in ascending order?
  3. The semicircle below represents a vegetable garden. It was fenced with five strands of wire.

What length of wire was used? (Take π=22/7)

  1. Mwakio bought an item after being offered a discount of 30%. If this discount represented a reduction of sh 210, what was the price of the item before the discount?
  2. What is the next number in the pattern 5, 12, 19, 26, _____ ?
  3. What is the value of 6c − (b − a) when a = 4, b = a+2 and c=½a + 3?

b + c

  1. The figure below is an incomplete triangle PQR. Complete the triangle such that line

PQ=6cm and PR=7cm. Draw a circle whose circumference touches the points P, Q and R.

What is the radius of the circle?

  1. The marked price of a table is sh 20000. The hire purchase price is 40% more than the marked price. Wasike bought the table on hire purchase terms by paying a deposit of sh 15000 and the balance in 5 equal monthly installments. How much was each monthly installment?
  2. What is the Least Common Multiple of 24, 30 and 60?
  3. A trader had a tonne of salt. He repacked the salt into equal number of 200g and 300g packets. How many packets did he get altogether?
  4. Onyango earns a basic salary of sh 40000 per month plus a commission of 6% on the sale of goods above sh 50000. In one month he sold goods worth sh 300000. How much altogether did he earn that month?
  5. A bus left town Q for town R a distance of 240km. It was driven at a speed of 80km/h. If it arrived at 2:40am, at what time did it depart from town Q?
  6. A rectangular tank measures 3m long, 2.8m wide and 2.5m high. What is the capacity of the tank in litres?
  7. In the triangle EFG below, bisect angle EGF to meet line EF at P.

What is the length of line GP?

  1. The median of eight numbers is 7. Seven of the numbers are 11,4,9,4,5,8 and 10. What is the eighth number?
  2. The price of a laptop decreased by sh 15000 to 25000. What was the percentage decrease?
  3. Wahondo performed as follows in a test;

Maths 80%, English 75%, Kiswahili 85%. Science 70%, SSTRE 90%. If he represented his scores in a pie chart. How many more degrees would represent SSTRE than Maths?

  1. The volume of a cylindrical tin is 2816cm3 and the height is 14cm. What is its diameter?

(Take π=22/7 )

  1. What is the value of x in the inequality

5x − 20 > 3x + 8?

  1. The table below shows how three teams performed in sports competition. The number of times each team was placed in either 1st, 2nd or 3rd position is as shown.
   1st  2nd  3rd
 Star   3   2   1
 Elite   3   3   5
 Shine   2   4   2

If 6 points were awarded for the first position, four points for the second position and 2 points for the third position. What was the total points scored by the three teams?

  1. How many groups of a hundred are there the total value of the digit in the thousands position in the smallest six-digit number formed using the digits 4,3,0, 5, 7, 1?
  2. Magelo and Olwande shared some fruits in the ratio 5:3 Magelo received 30 more fruits than Olwande. How many fruits did Magelo get?
  3. Milkio sold some of his properties to three people as follows: Kavunga got ¼ while Meso got 1/6 while Kioko received ½ of the remainder. What fraction of the properties did he sell?
  4. Which one of the following sets of measurements will form a right angled triangle? 183.The figure below shows a stack of cubes. The stack was painted all over.

How many cubes had paint on two faces only?

  1. A plane reached town Q from town on a Sunday at 0240hrs after travelling for 6 hrs 55mins. On what day and time did it leave town R?
  2. The length of road is 4.5km. The road is represented on a map by 3cm. What is the scale of the map?
  3. The fractions ½,⁷/₉,³/₈,⁵/₇ are to be arranged from the largest to the smallest. Which of the following is the correct order?
  4. At a function the number of women was twice that of men. The number of children was half the total number of men and women. The function was attended by 270 people. How many children attended the function?
  5. The table below shows the postal charges in shillings for small packets in a certain year.
 Mass of packet  East Africa  Rest of Africa  Rest of the world
Not over 20g

Not over 100g

Not over 250g

Not over 500g

Not over 1kg

Not over 2kg

Each additional

1kg upto 5kg

  49.00

98.00

187.00

319.00

529.00

728.00

364.00

   54.00

170.00

214.00

375.00

618.00

850.00

430.00

  68.00

154.00

275.00

482.00

768.00

1019.00

553.00

Mutunga sent the following packets

A 600g packet to Tanzania

A 4kg packet to Nigeria

A 260g packet to America  How much did he pay altogether?

  1. Twelve people can complete a piece of work in 20 days. How many more days will 8 people working at the same rate require to complete the same work?
  2. The following properties describe a certain quadrilateral
    • Diagonals are not equal
    • Sum of interior angles is 360°
    • Has a pair of parallel sides
    • Diagonals do not bisect each other.

Which quadrilateral has the above properties?

  1. The diagram below shows a wooden solid

Calculate the sure area taking π=3.14

  1. A motorist left town A for town B a distance of 120km at a speed of 60km/h. After 30 minutes he got a puncture which took 30 minutes to repair. After repair he travelled the remaining distance at a speed of 45km/h. What was his average speed for the whole journey?
  2. A rectangular plot of land is 80m long and the length of one diagonal is 100m. What is the area of the plot in hectares?
  3. Makau bought f fruits. Obach bought 5q more fruits than Makau while Ongeri bought three times the total bought by both Makau and Obach. How many fruits were bought by the three people altogether?
  4. In the figure below line AB is parallel to line CD and XY is a straight line, angle CKR = 110°, line RT RY.

What is the measure of angle YTB?

  1. Special porridge is made by mixing sorghum and millet in the ratio 2:3. Sorghum costs sh60 per kg and millet costs sh40 per kg. If Aisha made 10kg of special porridge, how much money did she spend on sorghum and millet altogether?
  2. Muunda bought 40 plates for sh 4160. He sold all the plates at a profit of 120% How much did he sell cach plate?
  3. Bongonko borrowed sh250000 from a bank that charged a simple interest at the rate of 20% per annum. How much interest did she earn altogether after 2 years?
  4. Mutua left Machakos at 8:15am and took 1 hours to travel to Emali. He stayed in Emali for 2 hours then travelled back to Machakos. The time taken to travel back to Machakos was half the time taken to travel to Emali. At what time did he arrive at Machakos?
  5. Construct triangle PQR in which PQ=6.7cm.Tem QR= 5.8 and PR=7.1cm,Bisect angle QRP and let the sector meet Line PQ at M.

What is the size of angle PRM?

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