Why settle the sign before calculating?

For directed numbers, decide the sign first and then work with the magnitudes: same signs add and keep the sign, opposite signs take the sign of the larger magnitude, and multiplication or division gives positive for like signs and negative for unlike signs.

What order should be used when substituting?

Put brackets round every substituted value, then work through brackets, indices, multiplication and division, and finally addition and subtraction. Keep −3² (which is −9) apart from (−3)² (which is 9).

S1 Maths: Directed Numbers and Algebra (Foundation, 10 Questions)

2026-11-06

Tutor Prep Guide · S1 Mathematics

Ten foundation items on the first operations with directed numbers: adding, subtracting, multiplying and dividing integers, distance on a number line, collecting like terms and substituting negative values into expressions, each with an answer and a short note.

Quick answer Answers in order: -8, 11, -12, 6, 6, 1, 8a, 6b, -1, 4. Settle the sign first, then work with the magnitudes.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 25 minutes
Difficulty mix	Foundation 10
Chapter	Chapter: S1 Maths: Directed Numbers and Algebra
Level	S1

02 Questions (10 items)

FoundationWork out (−3) + (−5).
FoundationWork out 7 – (-4).
FoundationWork out (-2) x 6.
FoundationWork out (-18) / (-3).
FoundationOn a number line, how many units apart are -2 and 4?
FoundationWork out -5 + 9 – 3.
FoundationSimplify 3a + 5a.
FoundationSimplify 7b – 2b + b.
FoundationFind the value of 2x + 5 when x = -3.
FoundationFind the value of y squared minus 3y when y = 4.

03 Answers and one-line notes

#	Answer	One-line note
1	-8	Adding two negative numbers keeps the negative sign: 3 + 5 = 8, so the answer is -8.
2	11	Subtracting a negative number is the same as adding its opposite: 7 + 4 = 11.
3	-12	Unlike signs give a negative product: 2 x 6 = 12, so the answer is -12.
4	6	Like signs give a positive quotient: 18 / 3 = 6.
5	6	The distance is the absolute value of the difference: 4 – (-2) = 6 units.
6	1	Working from left to right: -5 + 9 = 4, then 4 – 3 = 1.
7	8a	Add the coefficients of like terms: 3 + 5 = 8, so the result is 8a.
8	6b	A single b has coefficient 1, so 7 – 2 + 1 = 6 and the result is 6b.
9	-1	Substituting gives 2 x (-3) + 5 = -6 + 5 = -1.
10	4	First 4 squared is 16, then 3 x 4 = 12, and 16 – 12 = 4.

04 What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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