Daily Practice · Higher Plus
May 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1998Solve x^2 + 4x < 0.
- 2nd May 1998y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 3rd May 1998In a vector proof you find that vector PQ = 2a - 3b and vector RS = 6a - 9b. What does this show about PQ and RS?
- 4th May 1998A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 5th May 1998On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th May 1998A rectangle is 25 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th May 1998Write x^2 - 14x - 13 in the form (x + a)^2 + b.
- 8th May 1998y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 9th May 1998A cuboid measures 4 cm by 7 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th May 1998A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th May 1998A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 12th May 1998Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 13th May 1998Work out the coordinates of the turning point of y = x^2 - 14x - 15.
- 14th May 1998y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 64.
- 15th May 1998A cuboid measures 7 cm by 6 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th May 1998A bag holds 6 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th May 1998On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th May 1998A block has mass 250 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th May 1998Simplify (x^2 - 9)/(x + 3).
- 20th May 1998A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 21st May 1998The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 22nd May 1998A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 23rd May 1998A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 24th May 1998x = 129 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th May 1998In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 26th May 1998y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 27th May 1998In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 28th May 1998The probability of winning a game is 4/5. A player expects 48 wins. How many games did they play?
- 29th May 1998On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th May 1998A car covers 360 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st May 1998Make x the subject of 8x + 7 = y(x + 7).