Daily Practice · Higher Plus
March 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1998x = 53 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd March 1998Solve 9x^2 - 21x + 10 = 0.
- 3rd March 1998y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 4.
- 4th March 1998In a vector proof you find that vector PQ = 4a + b and vector RS = 16a + 4b. What does this show about PQ and RS?
- 5th March 1998A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 6th March 1998On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th March 1998A car covers 490 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th March 1998f(x) = 4x + 8. Work out the inverse function f^-1(x).
- 9th March 1998A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 10th March 1998A cuboid measures 15 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th March 1998A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th March 1998A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 13th March 1998Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 14th March 1998Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 15th March 1998y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 16th March 1998A cuboid measures 5 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th March 1998A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th March 1998On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th March 1998Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
- 20th March 1998Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 21st March 1998y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 22nd March 1998The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 23rd March 1998A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 24th March 1998A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 25th March 1998A rectangle is 10 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th March 1998Work out the nth term of the quadratic sequence -4, -3, 2, 11, ...
- 27th March 1998y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 25.
- 28th March 1998In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 29th March 1998The probability of winning a game is 3/10. A player expects 27 wins. How many games did they play?
- 30th March 1998On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 31st March 1998Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).