ĐỀ KIỂM TRA ĐẠI SỐ 10

KIỂM TRA 1 TIẾT
MÔN : ĐẠI SỐ
Điểm Lời phê của thầy
Câu 1 : Xác định tính đúng, sai của các mệnh đề sau : ( 2 điểm )
1) Số 3 là số chẵn.
2) Nếu a là số nguyên tố thì a có hai ước là 1 và chính nó.
3)
2
là số vô tỷ.
4) 34567 chia hết cho 9.
Câu 2 : Cho các mệnh đề P và Q. Phát biểu và xác định tính đúng, sai của mệnh đề P => Q.
( 2 điểm )
a) P : ABC là một tam giác cân.
Q : ABC là một tam giác đều.
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b) P : ABCD là một hình bình hành.
Q : ABCD là một hình thang.
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Câu 3 : Tìm tập xác định của các hàm số sau: ( 2 điểm )
a) y =
5
3
−
x
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b) y =
x28
−
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Câu 4 : Cho hàm số y = ax
2
+ bx + c . ( 4 điểm )
Họ và tên :……………………………...
Lớp 10A…
a) Xác định a, b, c biết rằng đồ thị của hàm số đi qua ba điểm: A(0 ; 3 ) ; B( 2 ; –5 ) ; C( –1 ; 4)
b) Vẽ đồ thị hàm số với a, b, c vừa tìm được.
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Đáp án:
Câu 1 : 1 – Sai ; 2 – Đúng ; 3 – Đúng ; 4 – Sai
Câu 2 :
a) P => Q : Nếu ABC là một tam giác cân thì ABC là một tam giác đều ( mệnh đề sai )
b) P => Q : Nếu ABCD là một hình bình hành thì ABCD là một hình thang ( mệnh đề đúng )
Câu 3 :
a) x – 5
≠
0 => x
≠
5. Vậy D = R \ { 5 }
b) 8 – 2x
4820
≤⇒−≥−⇒≥
xx
. Vậy D = (
∞−
; 4 ]
Câu 4 :
a) Vì đồ thị đi qua A( 0 ; 3 ) nên: c = 3. Khi đó hàm số có dạng y = ax
2
+ bx + 3

Vì đồ thị đi qua B( 2 ; –5 ) nên :
4a + 2b + 3 = –5
Vì đồ thị đi qua C( –1 ; 4) nên :
a – b + 3 = 4
Ta có hệ phương trình :





=
−=
−=
⇒





=+−
−=++
=
3
2
1
4 3 b a
5 3 2b 4a
3 c
c
b

a
Vậy : y = – x
2
– 2x + 3
b) Vẽ đồ thị hàm số y = – x
2
– 2x + 3
TXĐ : D = R
Toạ độ đỉnh : I ( – 1 ; 4 )
Trục đối xứng : x = –1
Giao điểm với Oy: A( 0 ; 3 )
Điểm đối xứng với A( 0 ; 3 ) qua đường x = –1 là A’(–2 ; 3)
Giao điểm với Ox: B(1 ; 0) và C( –3 ; 0 )
Bảng biến thiên :
x
∞−
–1
∞+
y
4
∞−

∞−
Đồ thị :