This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.
Using the same line graph (March 500, April 600, May 800, June 1100, July 800), what was the total number of books borrowed from March to June?
Mar Apr May Jun Jul 500 600 800 1100 800 |<---- March to June ---->|
answer 3000
method Add the four months named — March, April, May and June: 500 + 600 + 800 + 1100 = 3000 books. July is not included, because the question stops at June.
watch READ THIS ONE BEFORE TEACHING IT. The published answer key says 3800, which is the total of all FIVE months including July. For the question as printed — March to June — the answer is 3000. Check the wording with her rather than the key: if she answers 3000 she has read the question correctly.
The table shows the boys and girls in four Primary Four classes, with some cells blank: 4A has 22 boys and 18 girls; 4B has 25 girls and 41 students in total; 4C has 13 boys; 4D has 20 girls. There are as many students in Primary 4A as in Primary 4C. How many girls are there in Primary 4C?
Class | Boys | Girls | Total ------+------+-------+------ 4A | 22 | 18 | 4B | | 25 | 41 4C | 13 | | 4D | | 20 |
answer 27
method Fill in 4A first: 22 + 18 = 40 students. We are told 4C has as many students as 4A, so 4C also has 40. Of those, 13 are boys, so the girls number 40 − 13 = 27.
watch Comparing 4A's BOYS with 4C's boys. The sentence says as many STUDENTS, which means the totals match, not the boys.
Using the same table, the four classes have a total of 160 students. How many students are from the class that has the least number of students?
4A = 22 + 18 = 40 4B = 41 (given) 4C = 40 (same as 4A) 4D = ? all four classes together = 160
answer 39
method Three of the classes are now known: 4A = 40, 4B = 41, 4C = 40, which is 121 students. So 4D = 160 − 121 = 39. Comparing 40, 41, 40 and 39, the smallest is 4D with 39 students.
watch Stopping once 4D is found without checking it really is the smallest, or picking 4C's 13 boys as "the least". The question asks about whole classes.
John spilled some paint on his report card, hiding his Mathematics and Science scores. English was 86, Chinese was 80, and the total of all four subjects was 342. He scored 12 fewer marks in Science than in Mathematics. How many marks did he score for Mathematics?
Subject | Score -------------+------- English | 86 Chinese | 80 Mathematics | ##### Science | ##### Total | 342
answer 94
method Maths and Science together = 342 − 86 − 80 = 176. Science is 12 fewer than Maths, so take that 12 off and split the rest equally: (176 − 12) ÷ 2 = 164 ÷ 2 = 82 — that is Science. Maths = 82 + 12 = 94.
watch Splitting the 176 evenly into 88 and 88 and forgetting the 12, or adding the 12 to the wrong subject. Science is the SMALLER one.
The line graph shows the number of books borrowed by students in a library: March 500, April 600, May 800, June 1100, July 800. How many more books were borrowed in July than in March?
Mar Apr May Jun Jul 500 600 800 1100 800
answer 300
method Read July off the graph: 800. Read March: 500. "How many more" means subtract: 800 − 500 = 300.
watch Reading the peak (June, 1100) instead of July. Follow the month labels along the bottom, not the highest point.
The line graph shows the earnings at Mr Lim’s chicken rice stall over a 6-month period: January $3000, February $4500, March $5000, April $3500, May $3000, June $2500. Mr Lim charged $5 for every plate of chicken rice. What is the difference in the number of plates of chicken rice sold between the highest earnings month and the lowest earnings month?
Jan Feb Mar Apr May Jun 3000 4500 5000 3500 3000 2500 highest = March, lowest = June · $5 a plate
answer 500
method The highest month is March at $5000 and the lowest is June at $2500. The difference in money is $5000 − $2500 = $2500. Each plate is $5, so that is 2500 ÷ 5 = 500 plates.
watch Working out each month's plates and then subtracting is fine too (1000 − 500 = 500), but dividing the DIFFERENCE once is quicker. The real slip is reading May as the lowest — June is lower.
The table shows the favourite colours of 108 pupils in Primary Four. Some numbers have been blotted out by ink stains. There were twice as many pupils who chose green than yellow. There is a total of 38 pupils who like 2 of the colours. Which of the following options shows the two colours?
Colour | Number of Pupils -------+----------------- Green | ### stain ### Yellow | ### stain ### Blue | 22 Red | 38 108 pupils altogether · green = 2 × yellow
(1) Blue and Green (2) Yellow and Blue (3) Green and Red (4) Red and Yellow
answer (2) — Yellow and Blue
method Green and yellow together = 108 − 22 − 38 = 48. Green is twice yellow, so that is 3 equal shares: yellow = 48 ÷ 3 = 16 and green = 32. Now test the pairs: blue + green = 54, yellow + blue = 16 + 22 = 38 ✓, green + red = 70, red + yellow = 54.
watch Splitting the 48 evenly into 24 and 24. "Twice as many" makes THREE shares, not two.
The graph shows the number of watches sold by a shop from January to April: January 38, February 22, March 52, April 16. The total number of watches sold from January to April was 4 times the number of watches sold in May. How many watches were sold in May?
Jan Feb Mar Apr 38 22 52 16
(A) 31 (B) 32 (C) 54 (D) 64
answer (B) — 32
method Add the four months: 38 + 22 + 52 + 16 = 128 watches. That total is 4 times May's figure, so May = 128 ÷ 4 = 32 watches.
watch Multiplying by 4 instead of dividing. The four months together are the BIG number, so May must be smaller than it.
The table shows the number of pets kept by a group of children. How many children have MORE than 1 pet?
Number of pets | 0 | 1 | 2 | 3 | 4 -------------------+----+----+---+---+--- Number of children | 10 | 17 | 5 | 8 | 2
(A) 15 (B) 17 (C) 27 (D) 32
answer (A) — 15
method "More than 1 pet" means 2, 3 or 4 pets — not 1, and not 0. Add those three columns: 5 + 8 + 2 = 15 children.
watch Including the 17 children who have exactly 1 pet (giving 32). "More than 1" excludes 1 itself; "1 or more" would include it.
The table below shows the 3-h PSI readings from 8 am to 12 noon on 22nd February. Which one of the line graphs best represents the information in the table?
Time | 8 am | 9 am | 10 am | 11 am | 12 noon ----------+------+------+-------+-------+-------- 3-h PSI | 35 | 55 | 50 | 45 | 40 (1) starts high, dips, rises, then falls (2) starts low, jumps to the peak at 9 am, then falls every step (3) rises to a peak at 10 am, then falls (4) starts low, peaks at 9 am, falls, rises again at 11 am, then falls
(1) Graph (1) (2) Graph (2) (3) Graph (3) (4) Graph (4)
answer (2) — Graph (2)
method Describe the numbers before looking at the graphs: 35 → 55 is a sharp RISE, then 55 → 50 → 45 → 40 falls every single step. Only graph (2) starts low, jumps to its highest point at 9 am, and then goes down at every point after.
watch Picking (4), which rises again at 11 am. The table never rises after 9 am — checking the LAST few points is what separates (2) from (4).
The table shows how many cakes a shop sold on four days. How many more cakes were sold on the last two days than on the first two days?
Day Cakes Monday 24 Tuesday 18 Wednesday 31 Thursday 27
(A) 6 (B) 13 (C) 16 (D) 22 (E) 58
answer (C) — 16
method First two days: 24 + 18 = 42. Last two days: 31 + 27 = 58. The difference is 58 − 42 = 16.