Dossier A — Fluidité — Algebra

BronzeQuestions 1–20

1.
Find the value of $3x + 4$ when $x = 5$ .
2.
Simplify $7x \times 4$ .
3.
Expand $4(x + 3)$ .
4.
Expand $x(3x - 2)$ .
5.
Factorise $10x + 15$ .
6.
Factorise $6x^2 + 9x$ .
7.
Simplify $\dfrac{{a}x}{{b}}$ .
8.
Identify which is equivalent to $3(x + 4)$ : $(3x + 4)$ or $(3x + 12)$ ?
9.
Substitute $a = 4, b = -2$ into $ab + 5$ .
10.
Simplify $4p + 7q + 3p$ .
11.
Solve $5x = 60$ .
12.
Solve $x + 7 = 20$ .
13.
Solve $x - 5 = 8$ .
14.
Solve $\dfrac{x}{{a}} = 7$ .
15.
A function machine: $x \to \times 3 \to + 4 \to$ output. If output is 19, find $x$ .
16.
Solve $3x + 5 = 14$ .
17.
Solve $10 - x = 4$ .
18.
Check whether $x = 5$ is a solution to $2x + 3 = 13$ .
19.
Solve $-x = -8$ .
20.
Solve $4x = -20$ where $rhs$ may be negative.

SilverQuestions 21–40

21.
Substitute $x = 5, y = 10, z = -1$ into $2x + 3y - z$ .
22.
Expand and simplify $4(x + 3) + 5(x - 2)$ .
23.
Factorise $20x^2 - 4xy$ .
24.
Simplify $\dfrac{{a}x^2}{{b}x}$ .
25.
Simplify $\dfrac{{a}x + 9}{{c}}$ by factorising.
26.
Expand and simplify $-3(x - 4) - 2(x + 5)$ .
27.
Simplify $\dfrac{6ab}{9a}$ by cancelling common factors.
28.
Show that $3(x + y) + 5(x - y)$ is equivalent to $(c)x + (d)y$ . Find $c$ and $d$ for $a = 3, b = 5$ .
29.
Factorise $x^2 + 6x$ .
30.
Pete has three times as many songs on his phone as Sabrina. Sabrina has 120 fewer songs than Elena. Elena has $x$ songs. Write expressions for (a) Sabrina, (b) Pete.
31.
Solve $3x + 7 = 22$ .
32.
Solve $2(x + 3) = 14$ .
33.
Solve $5x - 5 = 2x + 10$ .
34.
Solve $\dfrac{x}{{a}} + 2 = 8$ .
35.
Solve $5(x - 4) = 25$ .
36.
Solve $\dfrac{{a}x + 3}{{c}} = 7$ .
37.
A kite has two pairs of sides $(2n + 1)$ cm and $(3n - 2)$ cm. The perimeter is 38 cm. Find $n$ .
38.
Solve $3x + 8 = -7$ when $c$ is negative.
39.
I think of a number. I multiply by 4 and add 6. The result is 30. What is my number?
40.
A rectangle has length $(x + 5)$ and width $(x - 1)$ . Its perimeter is 28 cm. Find $x$ .

GoldQuestions 41–60

41.
Expand $-3(x - 4) - (5x + 6)$ .
42.
Factorise fully $24x^2 + 16x$ .
43.
Simplify $\dfrac{{a}x^2 + 9x}{{c}x}$ .
44.
Show that the expressions $(x + 3)^2 - 9$ and $x^2 + 6x$ are equivalent by expanding the first.
45.
Factorise $a^2 b + a b^2$ .
46.
Substitute $x = -3, y = 2$ into $2x^2 - 3xy + y^2$ .
47.
Factorise $4(x + 3) + y(x + 3)$ .
48.
Simplify $\dfrac{{a}}{x} + \dfrac{{b}}{x}$ .
49.
Simplify $\dfrac{x}{3} + \dfrac{x}{4}$ .
50.
A rectangle has length $(2x + 3)$ and width $(x - 1)$ . Find a simplified expression for the perimeter, and evaluate when $x = 4$ .
51.
Solve $\dfrac{{a}x - 5}{{c}} = 7$ .
52.
Solve $3(x - 4) = 2(5 + x)$ .
53.
Solve $\dfrac{x}{{a}} - \dfrac{x}{{b}} = 5$ .
54.
Pete has 3 times as many songs as Sabrina, who has 120 fewer than Elena. If Pete has 300 songs, how many does Elena have?
55.
A student won 370 of 500 games, then won the next $x$ games. He has now won 75% overall. Find $x$ .
56.
Three consecutive integers sum to $96$ . Find them.
57.
Two angles in a triangle are $(2x + 10)°$ and $(3x - 20)°$ , and the third is $90°$ . Find $x$ .
58.
A square has perimeter $4(x + 3)$ cm. Find $x$ when the perimeter is 32 cm.
59.
Solve $4x + 8 = 2x - 12$ where this gives a negative solution.
60.
I think of a number. I double it and add 5. I then triple the result and subtract 2. The result is 28. Find my number.

PlatinumQuestions 61–80

61.
Expand and simplify $6x(x + 3) - 5(4x - 2)$ .
62.
Factorise $3x^2 + 12x + 9$ by first taking out a common factor.
63.
Simplify $\dfrac{{a}x^2 - 9x}{{c}x^2 + 6x}$ .
64.
In a rectangle, the two long sides are labelled $3y$ cm and $(y + 3)$ cm; the two short sides are labelled $z$ cm and $(3z - 4)$ cm. (a) Find $y$ . (b) Find $z$ .
65.
Two similar triangles have a side ratio of $\dfrac{x+2}{15} = \dfrac{x}{{d}}$ . Find $x$ .
66.
A student won 370 of his first 500 games and then won the next $x$ games. He has now won 75% of all games. Find $x$ .
67.
Factorise $a^2 - b^2$ (difference of squares).
68.
A field has dimensions $(x + 5)$ m by $(x + 2)$ m. Write an expression for its area, expand, and find the area when $x = 8$ .
69.
Find the value of $x$ for which the area of a square of side $x$ is equal to the perimeter $4x$ .
70.
Simplify $\dfrac{x + 3}{2} - \dfrac{x - 1}{3}$ .
71.
Solve $\dfrac{x + {a}}{{b}} = \dfrac{x - {c}}{{d}}$ .
72.
Solve $\dfrac{2x + 1}{3} = \dfrac{x - 2}{2}$ .
73.
A laptop costs $x$ chf. The shop applies a 20% discount, then adds 7.7% VAT. The final price is 861.60 chf. Find $x$ .
74.
Two pens and three pencils cost 5.40 chf. One pen and two pencils cost 3.20 chf. Find the cost of each item.
75.
A man is 4 times his son's age now. In 4 years he will be 3 times. Find their current ages.
76.
Solve $\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{3}{4}$ .
77.
Two consecutive integers have a product of 132. Find them by setting up and solving an equation.
78.
A bottle holds 1.5 L of squash mix at concentration $x$ % sugar. Adding 0.5 L of water reduces concentration to 9%. Find $x$ .
79.
Solve $5 - 2(3x - 4) = 7x - (x + 1)$ .
80.
A rectangle has length $(2x + 1)$ and width $x$ . Its area equals its perimeter. Find $x$ .

Pack A — Fluency

Pack A · Fluency