1. What is 4/8 written in its simplest form?
1/2
Divide the top and the bottom by the same number, 4. 4 divided by 4 is 1, and 8 divided by 4 is 2, so 4/8 = 1/2.
2. What is 0.3 + 0.4?
0.7
Line up the decimal points: 0.3 + 0.4 = 0.7. Three tenths plus four tenths makes seven tenths.
3. What is 50% of 20?
10
50% means half. Half of 20 is 10.
4. What is -3 + 5?
2
Start at -3 on the number line and move 5 steps to the right: -3, -2, -1, 0, 1, 2. You land on 2.
5. What is 2 + 3 x 4?
14
Multiplication happens before addition. First work out 3 x 4 = 12, then add 2 to get 14. Adding first, 2 + 3 = 5, then x 4, gives the wrong answer of 20.
6. Solve for x: x + 5 = 9
4
Subtract 5 from both sides: x + 5 - 5 = 9 - 5, so x = 4.
7. In the coordinate pair (3, 5), which number tells you how far up the point is?
5
A coordinate pair is written (x, y). The first number, 3, is how far across. The second number, 5, is how far up, so 5 tells you the height.
8. What is the area of a rectangle 4 cm long and 3 cm wide?
12 cm squared
Area of a rectangle is length times width: 4 x 3 = 12 cm squared. 7 would be if you added instead of multiplied, and 14 is actually the perimeter, not the area.
9. What do we call the distance from the centre of a circle to its edge?
Radius
The radius goes from the centre to the edge. The diameter is a full line across the circle through the centre, twice the radius.
10. What is the mode of this set of numbers: 2, 3, 3, 5, 7?
3
The mode is the number that appears most often. Here, 3 appears twice and every other number appears once, so the mode is 3.
11. What is 1/3 + 1/6?
1/2
Give both fractions the same denominator. 1/3 is the same as 2/6, so 2/6 + 1/6 = 3/6, which simplifies to 1/2. Adding the numerators and denominators straight across, 1 + 1 over 3 + 6, gives the wrong answer of 2/9.
12. Which of these is the largest: 0.4, 0.35, 0.099, 0.41?
0.41
Compare digit by digit after the decimal point. 0.41 has 4 tenths and 1 hundredth, just ahead of 0.4, which is the same as 0.40. 0.099 looks like it has more digits but is actually less than one tenth.
13. A jacket costs $80 and is reduced by 25%. What is the new price?
$60
Find 25% of $80: 80 divided by 4 is 20. That is the discount. Subtract it from the original price: 80 - 20 = $60. $20 is just the discount, not the new price.
14. A recipe uses flour and sugar in the ratio 3:1. If you use 300 g of flour, how much sugar do you need?
100 g
The ratio 3:1 means for every 3 parts flour there is 1 part sugar. 300 g of flour is 3 parts, so 1 part = 300 divided by 3 = 100 g of sugar.
15. What is -4 - (-6)?
2
Subtracting a negative is the same as adding a positive: -4 - (-6) = -4 + 6 = 2.
16. What is (2 + 3) x 4?
20
Brackets first: 2 + 3 = 5. Then multiply: 5 x 4 = 20.
17. Solve for x: 3x = 21
7
Divide both sides by 3: 3x divided by 3 equals 21 divided by 3, so x = 7.
18. What are the coordinates of the point 2 across and 4 up from the origin?
(2, 4)
Coordinates are written (across, up). Two across and four up is written (2, 4). Swapping them, (4, 2), would mean four across and two up instead.
19. What is the area of a triangle with a base of 10 cm and a height of 6 cm?
30 cm squared
Area of a triangle is half of base times height: (10 x 6) divided by 2 = 60 divided by 2 = 30 cm squared. Forgetting to halve gives the wrong answer of 60.
20. What is the volume of a cube with sides of 3 cm?
27 cm cubed
Volume of a cube is side times side times side: 3 x 3 x 3 = 27 cm cubed. Squaring instead of cubing gives 9, which is only the area of one face.
21. The diameter of a circle is 10 cm. What is its radius?
5 cm
The radius is always half the diameter: 10 divided by 2 = 5 cm.
22. What is the median of this set: 4, 9, 2, 7, 5?
5
Put the numbers in order first: 2, 4, 5, 7, 9. The median is the middle value, which is 5.
23. A bag has 3 red balls and 2 blue balls. What is the probability of pulling out a red ball, as a fraction?
3/5
There are 5 balls in total and 3 of them are red, so the probability is 3 out of 5, written 3/5.
24. What is 2/3 x 3/4?
1/2
Multiply the numerators together and the denominators together: (2 x 3) over (3 x 4) = 6/12, which simplifies to 1/2.
25. What is 3.6 divided by 4?
0.9
3.6 divided by 4 = 0.9. Think of it as 36 divided by 4 = 9, then put the decimal point back one place: 0.9.
26. Express 3/8 as a percentage.
37.5%
Divide 3 by 8 to get 0.375, then multiply by 100 to turn it into a percentage: 37.5%.
27. Two numbers are in the ratio 5:3 and add up to 40. What is the larger number?
25
The ratio 5:3 has 5 + 3 = 8 parts in total. Each part is worth 40 divided by 8 = 5. The larger share is 5 parts, so 5 x 5 = 25.
28. What is -6 x -3?
18
A negative times a negative is a positive: -6 x -3 = 18.
29. What is 20 - 4 x 3 + 2?
10
Do the multiplication first: 4 x 3 = 12. Then work left to right: 20 - 12 = 8, then 8 + 2 = 10.
30. Solve for x: 2x + 3 = 11
4
Subtract 3 from both sides: 2x = 8. Then divide both sides by 2: x = 4.
31. A point moves from (2, 3) to (2, 7). In which direction has it moved?
Straight up
The first number (x) has not changed, so the point has not moved sideways. The second number (y) went from 3 to 7, an increase, so it has moved straight up.
32. A trapezium has parallel sides of 8 cm and 12 cm, and a height of 5 cm. What is its area?
50 cm squared
Area of a trapezium is the average of the two parallel sides, multiplied by the height: (8 + 12) divided by 2 = 10, then 10 x 5 = 50 cm squared.
33. What is the volume of a rectangular box that is 5 cm long, 4 cm wide and 2 cm high?
40 cm cubed
Volume of a box, a cuboid, is length times width times height: 5 x 4 x 2 = 40 cm cubed.
34. A circle has a radius of 7 cm. Using circumference is about 2 x pi x radius, and pi is about 22/7, what is its circumference?
44 cm
Circumference = 2 x pi x radius. Using pi as about 22/7 makes the 7s cancel neatly: 2 x 22/7 x 7 = 2 x 22 = 44 cm.
35. What is the mean of these test scores: 6, 8, 7, 9, 5?
7
Add all the scores together: 6 + 8 + 7 + 9 + 5 = 35. Then divide by how many there are, 5: 35 divided by 5 = 7.
36. A car travels 120 km in 2 hours. What is its average speed?
60 km/h
Speed = distance divided by time. 120 km divided by 2 hours = 60 km/h.
37. What is 2 and 1/4 minus 3/4?
1 and 1/2
Turn 2 and 1/4 into an improper fraction first: 2 and 1/4 = 9/4. Now subtract: 9/4 - 3/4 = 6/4, which simplifies to 1 and 1/2.
38. A price increases from $40 to $50. What is the percentage increase?
25%
Find the increase: 50 - 40 = 10. Divide the increase by the original price: 10 divided by 40 = 0.25, which is 25%. Dividing by the new price instead, 10 divided by 50, gives the wrong answer of 20%.
39. A map has a scale of 1:50,000. A distance on the map is 4 cm. What is the real distance, in kilometres?
2 km
Multiply the map distance by the scale: 4 cm x 50,000 = 200,000 cm. Convert to metres by dividing by 100: 2,000 m. Convert to kilometres by dividing by 1,000: 2 km.
40. What is (-2) cubed?
-8
(-2) cubed means -2 x -2 x -2. First, -2 x -2 = 4, since a negative times a negative is positive. Then 4 x -2 = -8, since a positive times a negative is negative.
41. What is 5 + (12 - 4) divided by 2 x 3?
17
Brackets first: 12 - 4 = 8. Then division and multiplication, left to right: 8 divided by 2 = 4, then 4 x 3 = 12. Finally add: 5 + 12 = 17.
42. Solve for x: 3(x + 2) = 18
4
First expand the brackets: 3(x + 2) = 3x + 6. So 3x + 6 = 18. Subtract 6 from both sides: 3x = 12. Divide by 3: x = 4.
43. A cylinder-shaped tin has a circular base of area 20 cm squared and a height of 10 cm. What is its volume?
200 cm cubed
For any prism or cylinder, volume is the area of the base times the height: 20 cm squared x 10 cm = 200 cm cubed.
44. A circular pizza has a diameter of 30 cm. What is its circumference, to the nearest whole centimetre, using pi as about 3.14?
94 cm
Circumference = pi x diameter. 3.14 x 30 = 94.2, which rounds to 94 cm. 47 cm is only the radius times pi, half of what is needed.
45. A set of numbers has a range of 12. The smallest number is 5. What is the largest number?
17
Range is the largest number minus the smallest: range = largest - smallest. Rearranged, largest = range + smallest = 12 + 5 = 17.
46. A spinner has 8 equal sections: 3 red, 2 blue, 3 green. What is the probability of NOT landing on blue, as a fraction?
3/4
6 of the 8 sections are not blue, that is the 3 red plus the 3 green. That is 6/8, which simplifies to 3/4. 1/4 would be the chance of landing ON blue, since 2/8 simplifies to 1/4.
47. In a class of 30 students, 40% play a sport and the rest do not. Of those who do not play a sport, half play a musical instrument. How many students play a musical instrument?
9
First find how many do not play a sport: 40% of 30 is 12, so 30 - 12 = 18 do not play a sport. Half of those 18 play an instrument: 18 divided by 2 = 9.
48. A cyclist rides 15 km at a steady speed of 20 km/h. How many minutes does the ride take?
45 minutes
Time = distance divided by speed = 15 divided by 20 = 0.75 hours. To turn 0.75 of an hour into minutes, multiply by 60: 0.75 x 60 = 45 minutes.
49. Solve for x: 5x - 3 = 2x + 9
4
Get the x terms on one side by subtracting 2x from both sides: 3x - 3 = 9. Then add 3 to both sides: 3x = 12. Divide by 3: x = 4.
50. A circular garden bed has a radius of 4 m. Using area is pi x radius squared, and pi is about 3.14, what is its area to the nearest whole square metre?
50 m squared
Area of a circle is pi times radius squared. First square the radius: 4 x 4 = 16. Then multiply by pi: 3.14 x 16 = 50.24, which rounds to 50 m squared. 25 m squared comes from treating the diameter as if it were the radius.