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Formal Formative: Algebra Criterion A

Last updated almost 3 years ago

8 questions

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Simple and Familiar (1 - 2)

Question 1

1.

Solve the following system of equations graphically.
3x+y = 9 and 5x+4y = 22

Question 2

2.

How many real solutions can the following quadratic equation have?
y2+16y+64=0

Complex and Familiar (3 - 4)

Question 3

3.

Choose the most efficient method (besides graphical) to solve the following system of equations.
3x+2y = 16 and 7x + y = 19

Question 4

4.

Solve for p in the quadratic equation, 2p2 - 4p -20 = 10

Challenging and Familiar (5 - 6)

Question 5

5.

A biotech company produces a new drug that consists of two key components, A and B. The drug is sold at two different rates based on the location of the buyer. The total price of the drug is determined by the ratio of components A and B in the formula.
Before the pandemic, the company used to charge $18 for every milligram of component A and $5 for component B, and a single standard dose costing $140. But after the pandemic and the increase in demand, the company now charges $15 for every milligram of component A and $2 for every milligram of component B. The total price for one dose is now only $120.
What is the ratio of components A and B in the formula and how much of each component is in one dose of the drug?

Question 6

6.

A model rocket is launched from 2.5 m above the ground with an initial velocity of 49m/s. Use the quadratic model h(t) = ½ * (-9.8)t2 + 49t + 2.5 to determine how long it takes for it to land.

Challenging and Unfamiliar (7 - 8)

Question 7

7.

Factorize this polynomial as far as possible and determine its roots:
(x+3x) (x2-11x+28) = 0

Question 8

8.

An architect constructs a building to resemble a parabola. The building has a vast circular garden surrounding it. A smaller parabolic gate at one end of the garden lets people into the parabolic spectacle. The shape of the building can be modelled by the equation
h (x) = -x2+20x-50, where h is the height of the building at a distance from the main gate and x is the distance from the main gate. Model an inequality to show at what distances from the gate you will be in the building and solve for x.