Daily Practice · Higher Plus
April 1960 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1960 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1960Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
- 2nd April 1960Work out the nth term of the quadratic sequence 15, 28, 47, 72, ...
- 3rd April 1960y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 25.
- 4th April 1960A cuboid measures 14 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th April 1960A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th April 1960On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th April 1960Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 8th April 1960The point (1, -5) lies on y = f(x). Write down its image on y = f(x) + 2.
- 9th April 1960A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
- 10th April 1960The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 11th April 1960A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 12th April 1960A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 13th April 1960A rectangle is 20 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th April 1960Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 15th April 1960y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 16th April 1960In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 17th April 1960The probability of winning a game is 3/8. A player expects 42 wins. How many games did they play?
- 18th April 1960On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th April 1960Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 20th April 1960f(x) = 3x - 5 and g(x) = 5x + 2. Work out fg(-2).
- 21st April 1960y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 22nd April 1960In a vector proof you find that vector PQ = 4a - 2b and vector RS = 16a - 8b. What does this show about PQ and RS?
- 23rd April 1960A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 24th April 1960A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 25th April 1960A block has mass 640 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th April 1960The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 27th April 1960y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 4.
- 28th April 1960A cuboid measures 5 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th April 1960A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th April 1960On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?