Daily Practice · Higher Plus
March 1975 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1975A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 2nd March 1975x = 110 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd March 1975Write x^2 - 14x + 5 in the form (x + a)^2 + b.
- 4th March 1975y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 25.
- 5th March 1975In a vector proof you find that vector PQ = 3a - 3b and vector RS = 9a - 9b. What does this show about PQ and RS?
- 6th March 1975A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 7th March 1975On 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?
- 8th March 1975A car covers 340 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th March 1975Work out the coordinates of the turning point of y = x^2 - 16x - 9.
- 10th March 1975A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 11th March 1975A cuboid measures 12 cm by 11 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th March 1975A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th March 1975A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 14th March 1975Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 15th March 1975Simplify (x^2 - 2x - 15)/(x + 3).
- 16th March 1975y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 17th March 1975A cuboid measures 12 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th March 1975A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th March 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th March 1975Simplify sqrt(80) + sqrt(245), giving your answer in the form a sqrt(b).
- 21st March 1975In an algebraic proof, how would you write an odd number in terms of an integer n?
- 22nd March 1975y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 23rd March 1975The 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.
- 24th March 1975A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 25th March 1975A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 26th March 1975A rectangle is 27 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th March 1975Make x the subject of 6x + 6 = y(x + 6).
- 28th March 1975y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 25.
- 29th March 1975In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 30th March 1975The probability of winning a game is 1/10. A player expects 10 wins. How many games did they play?
- 31st March 1975On 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?