Daily Practice · Higher Plus
March 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2005f(x) = 4x + 9. Work out the inverse function f^-1(x).
- 2nd March 2005y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 3rd March 2005A cuboid measures 12 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th March 2005A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th March 2005On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th March 2005x = 143 and y = 60, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th March 2005Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 8th March 2005y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 9th March 2005A cuboid measures 13 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th March 2005A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th March 2005A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 12th March 2005A car covers 110 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th March 2005Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 14th March 2005y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 4.
- 15th March 2005The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 16th March 2005A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 17th March 2005On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th March 2005Rationalise the denominator of 30/sqrt(5), giving your answer in its simplest form.
- 19th March 2005Work out the nth term of the quadratic sequence 2, 5, 10, 17, ...
- 20th March 2005A train slows steadily from 36 m/s to rest in 5 seconds. Work out its deceleration.
- 21st March 2005In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 22nd March 2005The probability of winning a game is 9/10. A player expects 90 wins. How many games did they play?
- 23rd March 2005A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 24th March 2005Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 25th March 2005The point (-5, -1) lies on y = f(x). Write down its image on y = f(-x).
- 26th March 2005y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 27th March 2005In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 28th March 2005A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 29th March 2005On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th March 2005A rectangle is 24 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st March 2005Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.