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Algebraic Methods · Part 4 of 4
6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on this part of the standard, grouped by the 2 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
The perimeter of a rectangle is 46 cm and its length is 7 cm more than its width. Form an equation and find its dimensions.
A rectangular sheet of card measures 20 cm by 14 cm. A border of uniform width is left around the outside and the remaining central rectangle has an area of 112 cm2. Find the width of the border.
The height of a ball thrown from a cliff is modelled by , where is the height in metres above sea level and is the time in seconds. The ball is released from a height of 30 m, reaches its maximum height of 50 m after 2 seconds, and the coefficient represents half the (negative) acceleration due to gravity. Find , and , and determine when the ball hits the sea.
A car bought for $32 000 depreciates at 18% per year. Find its value after 4 years.
A KiwiSaver balance of $22 000 grows at 6% per annum. How many complete years until it first exceeds $40 000?
Two investments are offered on $10 000: Option A pays 6% per annum compounded annually; Option B pays 5.8% per annum compounded monthly. Determine which is better, find the difference after 10 years, and find the annual rate that Option A would need to match Option B exactly.