Daily Practice · Higher Plus
April 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1990 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1990Write x^2 - 6x + 6 in the form (x + a)^2 + b.
- 2nd April 1990y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 3rd April 1990The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 4th April 1990A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 5th April 1990On 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?
- 6th April 1990Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 7th April 1990Work out the coordinates of the turning point of y = x^2 - 8x + 10.
- 8th April 1990y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 9th April 1990In 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.
- 10th April 1990The probability of winning a game is 3/4. A player expects 6 wins. How many games did they play?
- 11th April 1990A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 12th April 1990Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 13th April 1990Simplify (x^2 - 9)/(x + 3).
- 14th April 1990y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 25.
- 15th April 1990In a vector proof you find that vector PQ = 4a - 4b and vector RS = 16a - 16b. What does this show about PQ and RS?
- 16th April 1990A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 17th April 1990On 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?
- 18th April 1990A rectangle is 8 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th April 1990In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 20th April 1990A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 21st April 1990A cuboid measures 8 cm by 3 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd April 1990A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd April 1990A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 24th April 1990Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 25th April 1990Make x the subject of 7x + 6 = y(x + 6).
- 26th April 1990y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 27th April 1990A cuboid measures 14 cm by 6 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th April 1990A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th April 1990On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th April 1990A block has mass 510 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.