Head To Head: Year 7 Algebraic Simplification Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com Last Updated: 7th October 2015

vs Head to Head Head Table 8 9 Rear Table 2 7 10 15 3 6 11 14 4 5 12 You are head to head with the person on your table. You must circle or underline your answer to finalise it. Once you finalise an answer, you can’t change it. The first person with the correct answer wins. If both people get it wrong or neither answers, just do a quick paper-scissors-rock to settle. Winner moves up (as per left). Loser moves down. The winner on the head table stays where they are. If an odd number of people, have a single ‘King’ at the head table is not in competition for that round, and automatically moves down the next round. vs Head Table 8 9 Rear Table 2 7 10 15 3 6 11 14 4 5 12 13

(Click above to reveal answer) Question 1 Simplify 3 𝑥 2 +9𝑥−2𝑥+ 𝑥 2 ? 𝟒 𝒙 𝟐 +𝟕𝒙 (Click above to reveal answer)

(Click above to reveal answer) Question 2 Simplify 5𝑥×5𝑥𝑦 ? 𝟐𝟓 𝒙 𝟐 𝒚 (Click above to reveal answer)

(Click above to reveal answer) Question 3 Simplify −3𝑥𝑦 2 ? 𝟗 𝒙 𝟐 𝒚 𝟐 (Click above to reveal answer)

(Click above to reveal answer) Question 4 What is the perimeter of this rectangle in terms of 𝑥 and/or 𝑦? 𝑥−𝑦 3𝑦−𝑥 ? 𝟒𝒚 (Click above to reveal answer)

(Click above to reveal answer) Question 5 If 𝑎=−1, 𝑏=−2, 𝑐=3, what is the value of: 𝑏 2 −𝑎𝑐 ? 𝟒−−𝟑=𝟕 (Click above to reveal answer)

(Click above to reveal answer) Question 6 Fully simplify 8 𝑥 2 2𝑥 ? 𝟒𝒙 (do not accept 𝟒𝒙 𝟏 ) (Click above to reveal answer)

(Click above to reveal answer) Question 7 If 𝑥=−3, 𝑦=4, 𝑧=5, what is the value of: 𝑥𝑦+𝑥𝑧 ? −𝟏𝟐+−𝟏𝟓=−𝟐𝟕 (Click above to reveal answer)

(Click above to reveal answer) Question 8 If the cost of a cat is £𝑐, the cost of a dog is £3 less than that of a cat, and the cost of a giraffe is 5 times that of a cat. What is the cost (in terms of 𝑐) of 1 cat, 1 dog and 3 giraffes? (You must simplify your expression) ? 𝒄+𝒄−𝟑+𝟑 𝟓𝒄 =𝟏𝟕𝒄−𝟑 (Click above to reveal answer)

(Click above to reveal answer) Question 9 Fully simplify 3 𝑥 2 +3𝑥×3𝑥−1 ? 𝟏𝟐 𝒙 𝟐 −𝟏 (Click above to reveal answer)

(Click above to reveal answer) Question 10 𝐶 1 and 𝐶 2 are the centres of the large and small circle respectively. They have radii 𝑎 and 𝑏 as indicated. Determine (in terms of 𝑎 and 𝑏) the distance from 𝑪 𝟏 to 𝑪 𝟐 𝑎 𝑏 𝑋 𝑌 𝐶 1 𝐶 2 ? 𝒂−𝒃 (Click above to reveal answer)

(Click above to reveal answer) Question 11 𝐶 1 and 𝐶 2 are the centres of the large and small circle respectively. They have radii 𝑎 and 𝑏 as indicated. Determine (in terms of 𝑎 and 𝑏) the distance from 𝑿 𝒕𝒐 𝒀 𝑎 𝑏 𝑋 𝑌 𝐶 1 𝐶 2 ? 𝟐𝒂−𝟐𝒃 (Click above to reveal answer)

(Click above to reveal answer) Question 12 𝐶 1 and 𝐶 2 are the centres of the large and small circle respectively. They have radii 𝑎 and 𝑏 as indicated. Determine (in terms of 𝑎 and 𝑏) the distance from 𝒀 𝒕𝒐 𝑪 𝟏 𝑎 𝑏 𝑋 𝑌 𝐶 1 𝐶 2 ? 𝟐𝒃−𝒂 or −𝒂+𝟐𝒃 (Click above to reveal answer)

(Click above to reveal answer) Question 13 Fully simplify 4𝑥×3𝑦−3𝑥+ 9𝑥 𝑦 2 3𝑦 ? 𝟏𝟓𝒙𝒚−𝟑𝒙 (Click above to reveal answer)

(Click above to reveal answer) Question 14 A class has 𝑛 students each with an average (mean) of 60 on a maths test. A new student joins the class and scores 78, raising the average to 62. Give two different expressions for the total number of marks in the class (in terms of 𝑛). ? 𝟔𝟎𝒏+𝟕𝟖 𝒂𝒏𝒅 𝟔𝟐(𝒏+𝟏) Accept 62𝑛+62 (Click above to reveal answer)

(Click above to reveal answer) Question 15 The sum of each row/total is the same expression. Determine the expression that the ? represents. 𝑥−𝑦 𝑥+𝑦 3 ? 𝟑𝒙−𝟑𝒚 ? 3𝑥−𝑦 (Click above to reveal answer)