Daily Practice · Higher Plus
April 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1996 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1996The 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.
- 2nd April 1996A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 3rd April 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 4th April 1996Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
- 5th April 1996Use the iteration x(n+1) = cube root of (12x(n) + 5) with x(0) = 2. Work out x(1) to 3 decimal places.
- 6th April 1996y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 4.
- 7th April 1996In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 8th April 1996The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?
- 9th April 1996On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th April 1996A rectangle is 27 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th April 1996Work out the nth term of the quadratic sequence 10, 15, 22, 31, ...
- 12th April 1996A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
- 13th April 1996In a vector proof you find that vector PQ = 4a + 6b and vector RS = 20a + 30b. What does this show about PQ and RS?
- 14th April 1996A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 15th April 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 16th April 1996Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 17th April 1996The point (0, -3) lies on y = f(x). Write down its image on y = f(x) + 5.
- 18th April 1996y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 19th April 1996A cuboid measures 8 cm by 8 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th April 1996A 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?
- 21st April 1996On 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?
- 22nd April 1996A block has mass 520 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd April 1996Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 24th April 1996y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 25th April 1996A cuboid measures 6 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th April 1996A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th April 1996A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 28th April 1996x = 30 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th April 1996f(x) = 5x - 3 and g(x) = 5x + 6. Work out fg(-2).
- 30th April 1996y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 16.