Daily Practice · Higher Plus
May 1977 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1977A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 2nd May 1977A block has mass 760 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.
- 3rd May 1977f(x) = 3x - 1 and g(x) = 3x + 6. Work out fg(1).
- 4th May 1977y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 25.
- 5th May 1977A cuboid measures 5 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th May 1977A bag holds 7 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th May 1977On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th May 1977x = 58 and y = 41, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th May 1977The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 10th May 1977A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.
- 11th May 1977The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 12th May 1977A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 13th May 1977A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 14th May 1977A car covers 400 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th May 1977A quadratic sequence starts 7, 14, 25, 40. Work out the second difference, and the coefficient of n^2.
- 16th May 1977y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 17th May 1977In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 18th May 1977The probability of winning a game is 1/8. A player expects 7 wins. How many games did they play?
- 19th May 1977On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th May 1977Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 21st May 1977Solve x^2 + 3x + 2 > 0.
- 22nd May 1977y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 23rd May 1977In a vector proof you find that vector PQ = a + 3b and vector RS = 2a + 6b. What does this show about PQ and RS?
- 24th May 1977A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 25th May 1977A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 26th May 1977Simplify sqrt(45) + sqrt(80), giving your answer in the form a sqrt(b).
- 27th May 1977Write x^2 + 2x + 2 in the form (x + a)^2 + b.
- 28th May 1977y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 36.
- 29th May 1977A cuboid measures 10 cm by 9 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th May 1977A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st May 1977On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?