Daily Practice · Higher Plus
March 1997 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1997f(x) = 6x + 1 and g(x) = 3x + 4. Work out fg(0).
- 2nd March 1997y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 3rd March 1997In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 4th March 1997The probability of winning a game is 3/4. A player expects 90 wins. How many games did they play?
- 5th March 1997A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 6th March 1997Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 7th March 1997The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 8th March 1997y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 36.
- 9th March 1997In a vector proof you find that vector PQ = 6a + 2b and vector RS = 12a + 4b. What does this show about PQ and RS?
- 10th March 1997A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 11th March 1997On 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?
- 12th March 1997A rectangle is 27 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th March 1997A quadratic sequence starts 6, 11, 20, 33. Work out the second difference, and the coefficient of n^2.
- 14th March 1997A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 15th March 1997A cuboid measures 15 cm by 8 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th March 1997A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th March 1997A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 18th March 1997Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 19th March 1997Solve x^2 - 12x + 20 < 0.
- 20th March 1997y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 21st March 1997A cuboid measures 14 cm by 9 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd March 1997A 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?
- 23rd March 1997On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th March 1997A block has mass 220 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th March 1997Write x^2 + 4x - 13 in the form (x + a)^2 + b.
- 26th March 1997y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 27th March 1997The 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.
- 28th March 1997A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 29th March 1997A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 30th March 1997x = 91 and y = 39, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st March 1997Work out the coordinates of the turning point of y = x^2 + 2x + 13.