ENLA Secondary Practice (Peru) ยท Mathematics

Problem Solving in Mathematics

121 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 121 questions

  1. A school notebook costs S/ 4.50. How much do 6 of these notebooks cost in total?
  2. A rectangular garden is 12 m long and 7 m wide. What is its perimeter?
  3. The ages of five cousins are 4, 8, 6, 10 and 12 years. What is their mean age?
  4. Solve for : .
  5. A bag holds 3 red, 5 blue and 2 green marbles. One marble is drawn at random. What is the probability that it is red?
  6. A jacket priced at S/ 150 has a 20% discount. How much does the customer pay?
  7. On a map with scale 1 : 50 000, two towns are 4 cm apart. What is the real distance between them?
  8. How many grams are there in 3.5 kg?
  9. Five workers can build a wall in 12 days, all working at the same rate. How many days would 8 workers need for the same wall?
  10. What are the solutions of ?
  11. A circular fountain has radius 7 m. Using , what is the area of its surface?
  12. Six students scored 3, 9, 4, 7, 12 and 5 on a quiz. What is the median score?
  13. A phone's price rises by 10% and the next month falls by 10%. Compared with the original price, the final price is:
  14. A line has slope 2 and passes through the point (0, 3). What is the value of when ?
  15. A right triangle has legs of 9 cm and 12 cm. What is the length of the hypotenuse?
  16. A savings account pays 6% simple interest per year. How much interest does S/ 2000 earn in 3 years?
  17. Two numbers satisfy and . What is the product ?
  18. A bus travels 150 km in 2.5 hours at a constant speed. What is its speed?
  19. Two fair dice are rolled. What is the probability that the sum is 8?
  20. A water tank is 50 cm long, 40 cm wide and 30 cm high. How many litres does it hold when full? (1 L = 1000 cm)
  21. Which values of satisfy ?
  22. What is of 80 minus of 80?
  23. A shop sells these numbers of juice bottles in a week: 2, 3, 3, 5, 3, 7, 5. What is the mode?
  24. The price of a ticket rises from S/ 40 to S/ 50. What is the percentage increase?
  25. The angles of a triangle are , and degrees. What is the size of the largest angle?
  26. An arithmetic sequence begins 5, 9, 13, 17, ... What is the 10th term?
  27. A 1.5 m tall student casts a shadow 2 m long. At the same moment a tree casts a shadow 12 m long. How tall is the tree?
  28. Simplify .
  29. A rectangular terrace is 3 m longer than it is wide, and its area is 70 m. What is its width?
  30. Tap A fills a tank in 6 hours and tap B fills it in 3 hours. A drain C empties a full tank in 12 hours. With all three open, how long does an empty tank take to fill?
  31. A shopkeeper buys a shirt for S/ 80, marks it up by 25% and then gives a 10% discount on the marked price. What is the profit as a percentage of the cost?
  32. The mean of five numbers is 12. A sixth number is added and the mean of the six numbers becomes 13. What is the sixth number?
  33. A bag has 4 red and 6 blue marbles. Two marbles are drawn one after the other without replacement. What is the probability that both are red?
  34. A theatre sold 30 tickets for S/ 300. Adult tickets cost S/ 12 and student tickets cost S/ 8. How many adult tickets were sold?
  35. A 10 m ladder leans on a wall with its foot 6 m from the wall. The top slides down 2 m. How far does the foot move away from the wall?
  36. A car drives from town A to town B at 60 km/h and returns along the same road at 40 km/h. What is its average speed for the whole round trip?
  37. The sum of two numbers is 7 and their difference is 1. What is the larger number?
  38. Solve . What is ?
  39. A cyclist rides to a village at 20 km/h and returns by the same road at 30 km/h. What is the average speed for the whole trip?
  40. What is the total surface area of a cuboid measuring 8 cm by 7 cm by 5 cm?
  41. A rectangular screen is 20 cm wide and 48 cm high. What is the length of its diagonal?
  42. After a discount of 40% a bike costs 300 soles. What was the price before the discount?
  43. The base of a prism is a right triangle with legs of 5 cm and 12 cm, and the prism is 8 cm high. What is its volume?
  44. Solve the equation . What is ?
  45. Solve . What is ?
  46. What is 10% of 80?
  47. A jacket costs 400 soles. During a sale the price is reduced by 50%. What is the new price?
  48. Anna and Piotr share 91 stickers in the ratio . How many stickers does Anna get?
  49. A bus travels at an average speed of 72 km/h for 3 hours. How far does it travel?
  50. A train covers 120 km at a constant speed of 60 km/h. How long does the journey take?
  51. A rectangle has sides of 15 cm and 11 cm. What is its area?
  52. A right triangle has legs of 8 cm and 15 cm. How long is the hypotenuse?
  53. A cuboid is 7 cm long, 7 cm wide and 6 cm high. What is its volume?
  54. Two angles of a triangle measure 43ยฐ and 46ยฐ. What is the third angle?
  55. What is the sum of the interior angles of a polygon with 5 sides?
  56. What is the mean of the numbers 4, 15, 16, 8, 20, 9?
  57. What is the median of 36, 29, 28, 20, 35?
  58. A bag has 8 red, 8 blue and 3 green balls. One ball is drawn at random. What is the probability that it is red?
  59. Which expression equals ?
  60. What is ?
  61. Convert 1.2 km to metres.
  62. What is the value of when ?
  63. Marta is 10 years old. Her mother is 2 times as old as Marta. How old will Marta's mother be in 7 years?
  64. A phone costs 800 soles. The shop raises the price by 20% and later lowers the new price by 25%. What is the final price?
  65. The sum of two numbers is 11 and their difference is 1. What is the larger number?
  66. Solve . What is ?
  67. A cyclist rides to a village at 40 km/h and returns by the same road at 60 km/h. What is the average speed for the whole trip?
  68. What is the total surface area of a cuboid measuring 2 cm by 4 cm by 6 cm?
  69. A rectangular screen is 9 cm wide and 12 cm high. What is the length of its diagonal?
  70. After a discount of 10% a bike costs 360 soles. What was the price before the discount?
  71. The base of a prism is a right triangle with legs of 8 cm and 10 cm, and the prism is 11 cm high. What is its volume?
  72. Solve the equation . What is ?
  73. Solve . What is ?
  74. What is 30% of 160?
  75. A jacket costs 50 soles. During a sale the price is reduced by 40%. What is the new price?
  76. In a class of 150 students, 30 come to school by bike. What percentage of the class is that?
  77. Anna and Piotr share 56 stickers in the ratio . How many stickers does Anna get?
  78. A bus travels at an average speed of 80 km/h for 2 hours. How far does it travel?
  79. A train covers 120 km at a constant speed of 40 km/h. How long does the journey take?
  80. A rectangle has sides of 4 cm and 5 cm. What is its area?
  81. A triangle has a base of 7 cm and a height of 12 cm. What is its area?
  82. A right triangle has legs of 6 cm and 8 cm. How long is the hypotenuse?
  83. What is the circumference of a circle with radius 11 cm?
  84. A cuboid is 4 cm long, 8 cm wide and 2 cm high. What is its volume?
  85. Two angles of a triangle measure 59ยฐ and 56ยฐ. What is the third angle?
  86. What is the sum of the interior angles of a polygon with 8 sides?
  87. What is the mean of the numbers 13, 18, 19, 16, 9?
  88. What is the median of 18, 13, 5, 38, 27?
  89. A bag has 2 red, 7 blue and 2 green balls. One ball is drawn at random. What is the probability that it is red?
  90. What is ?
  91. Convert 0.75 km to metres.
  92. What is the value of when ?
  93. Marta is 9 years old. Her mother is 3 times as old as Marta. How old will Marta's mother be in 5 years?
  94. A phone costs 200 soles. The shop raises the price by 20% and later lowers the new price by 10%. What is the final price?
  95. Solve . What is ?
  96. What is the total surface area of a cuboid measuring 3 cm by 6 cm by 6 cm?
  97. A rectangular screen is 30 cm wide and 40 cm high. What is the length of its diagonal?
  98. After a discount of 25% a bike costs 225 soles. What was the price before the discount?
  99. The base of a prism is a right triangle with legs of 5 cm and 12 cm, and the prism is 6 cm high. What is its volume?
  100. Solve . What is ?

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