Daily Practice · Higher Plus
February 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2004 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2004In a vector proof you find that vector PQ = 4a + 4b and vector RS = 16a + 16b. What does this show about PQ and RS?
- 2nd February 2004A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 3rd February 2004On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th February 2004A rectangle is 6 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th February 2004Work out the nth term of the quadratic sequence 10, 20, 34, 52, ...
- 6th February 2004A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 7th February 2004A cuboid measures 15 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th February 2004A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th February 2004A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 10th February 2004Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 11th February 2004The point (3, -1) lies on y = f(x). Write down its image on y = f(x) - 4.
- 12th February 2004y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 13th February 2004A cuboid measures 5 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th February 2004A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th February 2004On 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?
- 16th February 2004A block has mass 330 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th February 2004Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 18th February 2004y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 19th February 2004The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 20th February 2004A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 21st February 2004A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 22nd February 2004x = 78 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd February 2004f(x) = 5x - 1 and g(x) = 4x - 1. Work out fg(0).
- 24th February 2004y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 25th February 2004In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 26th February 2004The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 27th February 2004On 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?
- 28th February 2004A car covers 490 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.
- 29th February 2004The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.