Homework

National 5 Mathematics homework set

Skills and mixed revision | 25-35 minutes | Mixed practice

Name:

Date:

Class:

Pupil instructions

Answer each question in your jotter or on the printed sheet. Show enough working for your teacher to see your method.

Simplify √576.
Support hint: Split into square factor times remaining factor.
After a 20% increase, a price is £24.00. What calculation finds the original price?
Support hint: Write multiplier = 1.2
A shape is enlarged by length scale factor 3. What is the area scale factor?
Support hint: Write k²
Supported practice: Expand and simplify 5(x + 8).
Support hint: Draw arrows to both terms.
Find the gradient between (0, 4) and (3, 10).
Support hint: Draw a small slope triangle.
For x² − 8x + 15 = 0, write the two roots.
Support hint: Check by substitution.
Simplify 7⁸ × 7²
Support hint: Write repeated factors.
Simplify (x² − 16) ÷ (x + 4)
Support hint: Write the two brackets first.
In a right triangle, opposite = 12 and hypotenuse = 24. Find sin θ
Support hint: Label SOHCAHTOA.
Consolidation: Substitute x = 9 into 6x − 9
Support hint: Write the substitution line.
Vector a = (9, 3) and b = (3, 9). Find a + b
Support hint: Line up components vertically.
Simplify √144.
Support hint: Split into square factor times remaining factor.

24
Take out the largest square factor, then check whether the remaining surd can simplify again.
£24.00 ÷ 1.2
Reverse percentages divide by the multiplier.
9
Area scale factor is the square of the length scale factor.
5x + 40
Multiply each term inside the bracket.
2
Gradient is change in y divided by change in x.
x = 3 or x = 5
Factorise, then set each bracket equal to zero.
7¹⁰
Add powers when multiplying the same base.
x − 4
Factorise the difference of two squares, then cancel the common factor.
12
sin θ = opposite / hypotenuse
45
Replace x with the given value, then calculate.
(12, 12)
Add corresponding components.
12
Take out the largest square factor, then check whether the remaining surd can simplify again.