Student Name
Class / Section
Grade / Year
Teacher
School
Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
Evaluate the expression 4x + 3y - 2xy for x = 3 and y = 5. Show your working.
(3 pts)
2.
A rectangular garden has length L = 3a + 2 meters and width W = a - 1 meters. Derive a simplified expression for its perimeter in terms of a, then find the perimeter when a = 4. Show your working.
(3 pts)
3.
A student buys 7 identical notebooks. Each notebook has a marked price of p, but there is a discount of 3 on each. Write an expression for the total cost and evaluate it when p = 18. Show your working.
(3 pts)
4.
Mira is 4 years less than twice Rehan’s age. In 5 years, the sum of their ages will be 54. Find their current ages. Show your algebraic steps.
(3 pts)
5.
Three consecutive even integers have a sum of 114. Find the integers. Show your working.
(3 pts)
6.
A saver deposits x this month and increases the deposit by 20 each subsequent month for a total of 6 months. Find a simplified expression for the 6-month total and evaluate it for x = 100. Show your working.
(3 pts)
7.
Matchstick squares in a row share sides: the first square needs 4 sticks; each additional square adds 3 sticks. Derive a formula for the number of sticks needed for n squares in a row and compute it for n = 12. Show your reasoning.
(3 pts)
8.
A jar has 2x + 7 marbles. They are packed into bags that hold 5 marbles each. For x = 8, find the number of completely filled bags and how many marbles remain. Show your steps.
(3 pts)
9.
A car travels at (v + 5) km/h for (t − 0.5) hours. Write the distance as an expression in v and t, then evaluate for v = 40 and t = 3. Show your working.
(3 pts)
10.
A rectangle has width w = l − 3 and perimeter P = 50 meters. Use P = 2(l + w) to find the length l. Show your algebraic steps.
(3 pts)
11.
A cafe sells a combo of 2 sandwiches and 1 juice. If a group orders n combos, express the total number of sandwiches and juices, then find both totals for n = 7. Show your working.
(3 pts)
12.
A rectangle’s area is A(x) = (x + 3)(x − 1). If x increases by 2, find the increase in area and evaluate it when x = 5. Show your working.
(3 pts)
13.
Adult tickets cost a each; child tickets cost (a − 40). A family buys 3 adult and 2 child tickets. Write the total cost in terms of a and evaluate it when a = 150. Show your working.
(3 pts)
14.
Evaluate (x − 2)(x + 3) − (x − 1)^2 at x = 6 by simplifying the expression first. Show all steps.
(3 pts)
15.
On day 1 a gardener plants 7 flowers; each day after that, 5 more flowers than the previous day. How many flowers are planted on day 20? Show your working.
(3 pts)
16.
A recipe mixes sugar and flour in a 2:3 ratio. If the total mass is 5k + 10 grams, find expressions for the sugar and flour masses, then compute both when k = 8. Show your steps.
(3 pts)
17.
A regular n-gon has side length s(n) = 0.5n + 1 meters. Write the perimeter as a function of n and evaluate it when n = 10. Show your working.
(3 pts)
18.
The product of a number and 6 decreased by the sum of the number and 4 equals 38. Find the number. Show your algebraic steps.
(3 pts)
19.
Notebooks cost 25 each; if you buy at least 5, a 10% discount applies to notebooks only. Pens cost 12 each with no discount. With a budget of 200, how much change remains after buying 5 notebooks and 3 pens? Show your working.
(3 pts)
20.
Two numbers have a sum of 37. The difference (larger − smaller) equals twice the smaller minus 5. Find both numbers. Show your working.
(3 pts)
21.
The simplified form of 3(x + 4) − 2(2x − 5) is
.
(3 pts)
22.
If P = 2l + 2w and w = 3l − 5, then P expressed only in terms of l is
.
(3 pts)
23.
If two consecutive odd integers are n and n + 2, then their product minus their sum simplifies to
.
(3 pts)
24.
If a = 2b − 3 and b = 5, then the value of 3a − b is
.
(3 pts)
25.
The perimeter of a regular 11-gon with side length s is
.
(3 pts)
26.
The expression equivalent to (x + y)^2 − (x − y)^2 is
.
(3 pts)
27.
If f(n) = 5n − 1 and g(n) = n^2, then f(g(3)) equals
.
(3 pts)
28.
In the expansion of (2x − 3)(x + 5), the coefficient of x is
.
(3 pts)
29.
For a rectangle with fixed area A and width w, the length expressed in terms of A and w is
.
(3 pts)
30.
For a path of n triangles where the first needs 3 sticks and each additional triangle adds 2, the total sticks needed as a function of n is
.
(3 pts)
31.
Simplify 4(x − 2y) + 3(2y − x) to
.
(3 pts)
32.
If x = 2y + 1 and y = 4, then x^2 − y equals
.
(3 pts)
33.
The sum of the first n odd numbers equals
.
(3 pts)
34.
The simplified value of 1/2(6x − 4) − 1/3(3x + 6) is
.
(3 pts)
35.
If a rectangle’s length increases by k and its width decreases by k, the new perimeter in terms of l, w, and k is
.
(3 pts)
36.
The solution for x in the equation 3(x − 4) = 2x + 5 is
.
(3 pts)
37.
If h(t) = t^2 − 4t, then the change h(t + 3) − h(t) simplifies to
.
(3 pts)
38.
The simplified form of (a + b + c) − (2a − b + 3c) is
.
(3 pts)
39.
If a square has the same perimeter as a rectangle with sides l and w, then the side length of the square is
.
(3 pts)
40.
For the sequence defined by T1 = 2 and Tn = Tn−1 + 3 (n ≥ 2), the nth term Tn equals
.
(3 pts)