Daily Practice · Higher Plus
April 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 1998 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1998The point (-2, -5) lies on y = f(x). Write down its image on y = f(x) - 3.
- 2nd April 1998A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd April 1998In a vector proof you find that vector PQ = 4a + 5b and vector RS = 12a + 15b. What does this show about PQ and RS?
- 4th April 1998A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th April 1998A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 6th April 1998A block has mass 210 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th April 1998Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 8th April 1998y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 9th April 1998A cuboid measures 8 cm by 5 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th April 1998A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th April 1998On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th April 1998x = 103 and y = 68, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th April 1998f(x) = 4x + 3 and g(x) = 6x + 4. Work out fg(-1).
- 14th April 1998y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 15th April 1998A cuboid measures 5 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th April 1998A bag holds 4 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th April 1998A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 18th April 1998A car covers 600 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th April 1998The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 20th April 1998y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 25.
- 21st April 1998The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 22nd April 1998A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 23rd April 1998On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th April 1998Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 25th April 1998A quadratic sequence starts -3, 1, 7, 15. Work out the second difference, and the coefficient of n^2.
- 26th April 1998A train slows steadily from 32 m/s to rest in 10 seconds. Work out its deceleration.
- 27th April 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 April 1998The probability of winning a game is 5/8. A player expects 10 wins. How many games did they play?
- 29th April 1998A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 30th April 1998Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).