Common Core HSA.CED.A.2 worksheet

Question 1

Which equation is the line through (−5, −5) with slope −5?

• A. y + 5 = 5(x + 5)
• B. y + 5 = −5(x + 5)
• C. y − 5 = −5(x − 5)
• D. x + 5 = −5(y + 5)

Question 2

An app sells subscriptions. At price p, it sells 96 − 3p per day, so revenue R = p(96 − 3p). What price maximises revenue?

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Question 3

Chloe's phone plan costs 4 more for each extra gigabyte of data. A month with 8 GB costs 51. Using cost = m × GB + b, find b, the fixed monthly charge.

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Question 4

An open box is made from a 18 cm square of card by cutting a square of side x cm from each corner and folding up. V = x(18 − 2x)². Find the maximum volume in cm³.

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Question 5

6 painters take 11 days to paint a school. How many days would 3 painters take, working at the same rate?

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Question 6

Find the x-intercept of −3x − 5y = 15. Type it like (4, 0).

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Question 7

A line has slope −2 and crosses the y-axis at 3. Write its equation as y = … (type the right-hand side).

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Question 8

A farmer has 104 m of fencing to make a rectangular pen against a straight wall (the wall is one side). If the two sides at right angles to the wall are x m, the area is A = x(104 − 2x). Find the maximum area in m².

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Question 9

Find the equation of the line through (0, −1) and (−2, 7). Type y = … (just the right-hand side).

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Question 10

y is directly proportional to x. When x = 3, y = 15. Find y when x = 4.

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Question 11

Fatima sketches x − 4y = 8 by joining its two intercepts. What is the area of the triangle formed by the line and the two axes?

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Question 12

Find the equation of the line through (0, −1) and (4, −13). Type the right-hand side of y = … .

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Question 13

Write y + 3 = 4(x − 4) in the form y = mx + b. Type the right-hand side.

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Question 14

Find the equation of the line through (−6, 0) and (3, −6). Type the right-hand side of y = … (fractions are fine).

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Question 15

A line passes through (1, 0) and (−3, 4). The point (−5, k) is also on the line. Find k.

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Question 16

Which equation is the line through (6, 4) with slope 5?

• A. y + 4 = 5(x + 6)
• B. y − 6 = 5(x − 4)
• C. y − 4 = 5(x − 6)
• D. x − 6 = 5(y − 4)